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Nonparametric Filtering of the Realised Spot Volatility: A Kernel-based Approach

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  • Dennis Kristensen

    () (School of Economics and Management, University of Aarhus, Denmark)

Abstract

A kernel weighted version of the standard realised integrated volatility es- timator is proposed. By different choices of the kernel and bandwidth, the measure allows us to focus on specific characteristics of the volatility process. In particular, as the bandwidth vanishes, an estimator of the realised spot volatility is obtained. We denote this the filtered spot volatility. We show con- sistency and asymptotic normality of the kernel smoothed realised volatility and the filtered spot volatility. The choice of bandwidth is discussed and data- driven selection methods proposed. A simulation study examines the finite sample properties of the estimators.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-02.

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Length: 33
Date of creation: 11 May 2007
Date of revision:
Handle: RePEc:aah:create:2007-02

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Diffusion; in-fill asymptotics; kernel estimation; nonparametric; spot volatility; realised volatility;

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References

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  1. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
  2. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  3. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
  5. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
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  7. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
  8. D. Blanke, 2002. "Estimation of Local Smoothness Coefficients for Continuous Time Processes," Statistical Inference for Stochastic Processes, Springer, vol. 5(1), pages 65-93, January.
  9. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
  10. Andreou, Elena & Ghysels, Eric, 2002. "Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation, and Empirical Results," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 363-76, July.
  11. Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-74, January.
  12. Bertsimas, Dimitris & Kogan, Leonid & Lo, Andrew W., 2000. "When is time continuous?," Journal of Financial Economics, Elsevier, vol. 55(2), pages 173-204, February.
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  14. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
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Citations

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Cited by:
  1. Isabel Casas & Irene Gijbels, 2009. "Unstable volatility functions: the break preserving local linear estimator," CREATES Research Papers 2009-48, School of Economics and Management, University of Aarhus.
  2. Morten L. Bech & Yvan Lengwiler, 2012. "The Financial Crisis and the Changing Dynamics of the Yield Curve," Working papers 2012/06, Faculty of Business and Economics - University of Basel.
  3. Kalnina, Ilze, 2011. "Subsampling high frequency data," Journal of Econometrics, Elsevier, vol. 161(2), pages 262-283, April.
  4. Almut Veraart, 2011. "How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?," AStA Advances in Statistical Analysis, Springer, vol. 95(3), pages 253-291, September.
  5. Mark Podolskij & Mathieu Rosenbaum, 2012. "Testing the local volatility assumption: a statistical approach," Annals of Finance, Springer, vol. 8(1), pages 31-48, February.
  6. Dennis Kristensen, 2008. "Uniform Convergence Rates of Kernel Estimators with Heterogenous, Dependent Data," CREATES Research Papers 2008-37, School of Economics and Management, University of Aarhus.
  7. Dennis Kristensen & Andrew Ang, 2009. "Testing Conditional Factor Models," CREATES Research Papers 2009-09, School of Economics and Management, University of Aarhus.
  8. Fulvio Corsi & Davide Pirino & Roberto Renò, 2008. "Volatility forecasting: the jumps do matter," Department of Economics University of Siena 534, Department of Economics, University of Siena.
  9. Cecilia Mancini & Vanessa Mattiussi & Roberto Reno', 2012. "Spot Volatility Estimation Using Delta Sequences," DiMaD Working Papers 2012-10, Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze.
  10. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels," Working Papers 08011, Concordia University, Department of Economics, revised Dec 2008.
  11. Sujin Park & Oliver Linton, 2012. "Estimating the Quadratic Covariation Matrix for an Asynchronously Observed Continuous Time Signal Masked by Additive Noise," FMG Discussion Papers dp703, Financial Markets Group.
  12. Bandi, Federico & Corradi, Valentina & Moloche, Guillermo, 2009. "Bandwidth selection for continuous-time Markov processes," MPRA Paper 43682, University Library of Munich, Germany.

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